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The Circumsphere Radius of a Cube is the radius of the sphere that contains the Cube in such a way that all the vertices of the Cube are touching the sphere. It represents the distance from the center of the cube to any of its vertices through the circumscribed sphere.
The calculator uses the formula:
Where:
Details: This formula derives from the relationship between the total surface area of a cube and its spatial dimensions. The total surface area of a cube with side length 'a' is 6a². The circumsphere radius can be found using the space diagonal of the cube (a√3), and then relating it to the surface area through mathematical derivation.
Tips: Enter the total surface area of the cube in square meters. The value must be positive and greater than zero. The calculator will compute the circumsphere radius of the cube.
Q1: What is the difference between circumsphere radius and insphere radius?
A: Circumsphere radius touches all vertices of the cube, while insphere radius touches the center of all faces (inscribed sphere).
Q2: How is this formula derived from basic cube properties?
A: Starting from TSA = 6a², we get a = √(TSA/6). The space diagonal is a√3, and circumsphere radius is half of the space diagonal.
Q3: What are typical values for circumsphere radius?
A: For a standard cube, the circumsphere radius is always larger than the side length, specifically r_c = (a√3)/2.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to cubes. Other polyhedra have different relationships between surface area and circumsphere radius.
Q5: What are the practical applications of calculating circumsphere radius?
A: Used in packaging design, 3D modeling, crystallography, and any application where objects need to fit within spherical containers or boundaries.